The Collaborative International Dictionary of English v.0.48:

Mildly \Mild"ly\, adv.
   In a mild manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

mildly
    adv 1: to a moderate degree; "he was mildly interested"
    2: in a gentle manner; "he talked gently to the injured animal"
       [syn: gently, mildly]

Moby Thesaurus II by Grady Ward, 1.0:

46 Moby Thesaurus words for "mildly":
   after a fashion, appreciably, at any rate, at best, at least,
   at most, at the least, at the most, at the outside, at worst,
   comparatively, detectably, fairly, gently, in a manner, in a way,
   in part, in some measure, incompletely, leastwise, like a lamb,
   meekly, merely, moderately, modestly, not comprehensively,
   not exhaustively, only, pacifically, part, partially, partly,
   peaceably, pro tanto, purely, quietly, relatively, simply, so far,
   somewhat, tamely, thus far, to a degree, to some degree, tolerably,
   visibly